A Joint Modeling Approach for Right Censored High Dimensional Multivariate Longitudinal Data

Abstract

Analysis of multivariate longitudinal data becomes complicated when the outcomes are of high dimension and informative right censoring is prevailing. Here, we propose a likelihood based approach for high dimensional outcomes wherein we jointly model the censoring process along with the slopes of the multivariate outcomes in the same likelihood function. We utilized pseudo likelihood function to generate parameter estimates for the population slopes and Empirical Bayes estimates for the individual slopes. The proposed approach was applied to jointly model longitudinal measures of blood urea nitrogen, plasma creatinine, and estimated glomerular filtration rate which are key markers of kidney function in a cohort of renal transplant patients followed from kidney transplant to kidney failure. Feasibility of the proposed joint model for high dimensional multivariate outcomes was successfully demonstrated and its performance was compared to that of a pairwise bivariate model. Our simulation study results suggested that there was a significant reduction in bias and mean squared errors associated with the joint model compared to the pairwise bivariate model.

Keywords: Informative right censoring; Joint modeling; Likelihood based approach; Multivariate longitudinal outcomes; Random effect; Slope estimation.

Figure 1

(a–b): BUN, eGFR (a), and Serum creatinine mean levels (b) respectively plotted against follow-up months.

Figure 2

(a–b): BUN, eGFR (a), and Serum creatinine mean levels (b) respectively plotted against number of visits.